Algebras of multiplace functions for signatures containing antidomain

TL;DR

This paper introduces antidomain operations for algebras of multiplace partial functions and provides finite axiomatizations for their representation classes, including complexity results and the finite representation property.

Contribution

It defines antidomain operations for multiplace functions and offers finite axiomatizations for their representation classes, including injective functions, with complexity analysis.

Findings

Finite axiomatizations for representation classes.

Finite representation property holds for all classes.

Representation classes have coNP-complete equational theories.

Abstract

We define antidomain operations for algebras of multiplace partial functions. For all signatures containing composition, the antidomain operations and any subset of intersection, preferential union and fixset, we give finite equational or quasiequational axiomatisations for the representation class. We do the same for the question of representability by injective multiplace partial functions. For all our representation theorems, it is an immediate corollary of our proof that the finite representation property holds for the representation class. We show that for a large set of signatures, the representation classes have equational theories that are coNP-complete.